20100 marks19 questions
11 of its 19 questions are here. The rest have a figure or are still being checked, so for now they're only in the official PDF.
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Source: IIT-JEE 2010, Paper 2, Maths, published by JEE (Advanced). The official PDF
For r = 0, 1, ..., 10, let Aᵣ, Bᵣ and Cᵣ denote, respectively, the coefficient of xʳ in the expansions of (1+x)¹⁰, (1+x)²⁰ and (1+x)³⁰. Then ∑ᵣ₌₁¹⁰ Aᵣ (B₁₀Bᵣ − C₁₀Aᵣ) is equal to
Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to
Let f be a real-valued function defined on the interval (−1, 1) such that e⁻ˣ f(x) = 2 + ∫₀ˣ √(t⁴ + 1) dt, for all x ∈ (−1,1), and let f⁻¹ be the inverse function of f. Then (f⁻¹)′(2) is equal to
If the distance of the point P(1, −2, 1) from the plane x + 2y − 2z = α, where α > 0, is 5, then the foot of the perpendicular from P to the plane is
Two adjacent sides of a parallelogram ABCD are given by AB⃗ = 2î + 10ĵ + 11k̂ and AD⃗ = −î + 2ĵ + 2k̂. The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD′. If AD′ makes a right angle with the side AB, then the cosine of the angle α is given by
A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is
Two parallel chords of a circle of radius 2 are at a distance √3 + 1 apart. If the chords subtend at the center, angles of π/k and 2π/k, where k > 0, then the value of [k] is [Note: [k] denotes the largest integer less than or equal to k]
Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3. If ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r² is equal to